FLUID KINEMATICS F luid kinematics deals with describing the motion of fluids without nec- essarily considering the forces and moments that cause the motion. In this chapter, we introduce several kinematic concepts related to flow- ing fluids. We discuss the material derivative and its role in transforming the conservation equations from the Lagrangian description of fluid flow (following a fluid particle) to the Eulerian description of fluid flow (pertain- ing to a flow field). We then discuss various ways to visualize flow fields— streamlines, streaklines, pathlines, timelines, and optical methods schlieren and shadowgraph—and we describe three ways to plot flow data—profile plots, vector plots, and contour plots. We explain the four fundamental kine- matic properties of fluid motion and deformation—rate of translation, rate of rotation, linear strain rate, and shear strain rate. The concepts of vortic- ity, rotationality, and irrotationality in fluid flows are also discussed. Finally, we discuss the Reynolds transport theorem (RTT), emphasizing its role in transforming the equations of motion from those following a system to those pertaining to fluid flow into and out of a control volume. The anal- ogy between material derivative for infinitesimal fluid elements and RTT for finite control volumes is explained. • 121 CHAPTER 4 OBJECTIVES When you finish reading this chapter, you should be able to ■ Understand the role of the material derivative in transforming between Lagrangian and Eulerian descriptions ■ Distinguish between various types of flow visualizations and methods of plotting the characteristics of a fluid flow ■ Have an appreciation for the many ways that fluids move and deform ■ Distinguish between rotational and irrotational regions of flow based on the flow property vorticity ■ Understand the usefulness of the Reynolds transport theorem cen72367_ch04.qxd 10/29/04 2:23 PM Page 121
FLUID KINEMATICS
Jun 23, 2023
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